Numerical-simulation and conjunctive-management models of the Hunt-Annaquatucket-Pettaquamscutt stream-aquifer system, Rhode Island

Numerical-simulation and optimization techniques were used to evaluate alternatives for the conjunctive management of ground- and surface-water resources of the Hunt­-Annaquatucket­-Pettaquamscutt stream-aquifer system in central Rhode Island. Ground-water withdrawals from the Hunt-Annaquatucket-Pettaquamscutt aquifer exceeded 8 million gallons per day during months of peak water use during 1993­98, and additional withdrawals have been proposed to meet growing demands from within and outside of the system boundary. The system is defined by the Hunt­-Annaquatucket­-Pettaquamscutt aquifer, which is composed of glacial stratified deposits, and the network of rivers, brooks, and ponds that overlie and are in hydraulic connection with the aquifer. Nearly all of the water withdrawn, however, is derived from depletions of flow in the rivers, brooks, and ponds that overlie the aquifer. Streamflow depletions are of concern to environmental agencies because of the adverse effects that reductions in streamflow can have on aquatic and riparian ecosystems.

A conjunctive-management model of the stream-aquifer system was developed to simultaneously address the water-demand and streamflow-depletion issues. The objective of the model was to maximize total ground-water withdrawal from the aquifer during July, August, and September. These three months are generally the time of year when water-supply demands are largest and streamflows are simultaneously lowest. Total withdrawal from the aquifer was limited by a set of constraints specified in the model. These constraints were (1) maximum rates of streamflow depletion in the Hunt, Annaquatucket, and Pettaquamscutt Rivers; (2) minimum monthly water demands of each of three water-supply systems that withdraw water from the aquifer; and (3) minimum and maximum withdrawal rates at each supply well.

The conjunctive-management model was formulated mathematically as a linear program. The model was solved by a response-matrix technique that incorporates the results of transient, numerical simulation of the stream-aquifer system into the constraint set of the linear program. The basis of the technique was the assumption that streamflow-depletion rates in each river were a linear function of ground-water-withdrawal rates at each well. This assumption was shown to be valid for the conditions evaluated in this study, primarily because of the very high transmissivity of the aquifer near many of the wells pumped for water supply. A transient, numerical model of the system was developed to simulate an average annual cycle of monthly withdrawal and hydrologic conditions representative of the 56-year period 1941­96. The transient model was used to generate characteristic streamflow-depletion responses in each river to simulated withdrawals at each well; these characteristic responses, or response coefficients, were then incorporated directly into the streamflow-depletion constraints of the linear program.

Four sets of applications of the conjunctive-management model were made to determine whether total ground-water withdrawal from the aquifer during July, August, and September could be increased over the current total withdrawal for alternative definitions of the maximum rates of streamflow depletion allowed in the Hunt, Annaquatucket, and Pettaquamscutt Rivers. Current conditions were defined as the average monthly withdrawal rates at each supply well, water demands of each of the three water-supply systems, and estimated streamflow-depletion rates during the 6-year period 1993­98. Total withdrawal from all wells in the system from July through September during 1993­98 was 506.5 million gallons. Estimated streamflow-depletion rates for 1993­98 were calculated by use of the transient model, with the 1993­98 average monthly withdrawal rates specified at each supply well. Streamflow-depletion rates calculated for July, August, and September averaged 25 percent of the model-calculated pre-withdrawal streamflow rates for the Hunt River, 19 percent for the Annaquatucket River, and 7 percent for the Pettaquamscutt River.

The first set of applications of the model were made with the current estimated rates of streamflow depletion in the Hunt, Annaquatucket, and Pettaquamscutt Rivers. Results of these applications indicated that total withdrawal from the aquifer during July, August, and September could be increased from about 8 to 18 percent (from 546.0 to 596.3 million gallons) over the current total withdrawal. The increased withdrawal would require modifications to the current annual withdrawal schedule of each supply well and, for the 18-percent increase, a modified network of supply wells that would include two new wells in the Annaquatucket River Basin. A second set of model applications then was made to determine if current estimated rates of streamflow depletion in the Hunt River could be reduced without increasing current estimated rates of streamflow depletion in the Annaquatucket or Pettaquamscutt Rivers. Decreases in the current rates of streamflow depletion in the Hunt River would result in increased streamflow in the river during these three months. Results showed that current rates of streamflow depletion in the Hunt River during July, August, and September could be decreased from 5 to 15 percent, depending on whether the existing or modified well network was used.

Subsequent model applications indicated that substantial increases in total ground-water withdrawal from the aquifer are possible, but would require increased rates of streamflow depletion in the Annaquatucket and Pettaquamscutt Rivers. Maximum increases in the July through September withdrawal from the aquifer of about 39 to 50 percent (from 705.1 to 760.3 million gallons) over the current total withdrawal were calculated when streamflow-depletion rates in the Annaquatucket and Pettaquamscutt Rivers were allowed to increase from current estimated rates to a maximum of 25 percent of the model-calculated pre-withdrawal streamflow for each river during July, August, and September. Alternatively, it was shown that current estimated rates of streamflow depletion in the Hunt River during July, August, and September could be reduced by as much as 35 percent for the maximum allowed increases in streamflow depletion in the Annaquatucket and Pettaquamscutt Rivers; maximum increased withdrawal from the aquifer, however, would range from 8 to 18 percent over the current total withdrawal for the 35-percent reduction in streamflow-depletion rates in the Hunt River.

Results of the different applications of the model demonstrate the usefulness of coupling numerical-simulation and optimization techniques for regional-scale evaluation of water-resource management alternatives. The results of the evaluation must be viewed, however, within the limitations of the quality of data available for the Hunt­-Annaquatucket­-Pettaquamscutt stream-aquifer system and representation of the system by a simulation model. An additional limitation of the analysis was the use of an average annual cycle of monthly withdrawal and hydrologic conditions. Ground-water withdrawal strategies may need to be modified to meet streamflow-depletion constraints during extreme hydrologic events, such as droughts.

Contributing areas and sources of water to the supply wells also were delineated by use of a steady-state model of the stream-aquifer system. The model was developed to simulate long-term-average ground-water flow and ground-water/ surface-water interactions in the system during the 56-year period 1941­96. Sources of water to the wells consisted of precipitation and wastewater recharge to the aquifer, streamflow leakage from natural stream-channel losses, streamflow leakage caused by induced infiltration, and lateral ground-water inflow from till and bedrock upland areas.